Geometric characterization of locally corroded surfaces in steel bridge girders

The aging of steel bridge girders is often compounded by corrosion at girder ends due to leaking deck joints. With 6.8% of U.S. bridges in poor condition, there is an urgent need for accurate yet efficient methods to assess the residual load-bearing capacity of corroded girders. Traditional assessment methods often represent corrosion as uniform section loss or rely on simplified surface representations, compromising the accuracy of the residual capacity estimation. To address these limitations, this paper proposes a novel approach for characterizing the geometry of locally corroded steel surfaces by decomposing the corroded region into high-frequency (fine surface textures) and low-frequency (global shape) components using multilevel Lanczos filters. Validated using 3D scans collected from a 57-year-old in-service bridge, our case study shows that each high-frequency component can be modeled as a stationary random field using a Hole-Gaussian autocorrelation function, with correlation lengths inversely proportional to the cutoff frequencies of the Lanczos filters. The low-frequency component is accurately characterized by a bivariate Lagrange polynomial fitted via a 4 × 4 coefficient matrix, with average volume errors of less than 1% and normalized root mean square errors under 10% for most surfaces. The technique results in a manage set of parameters that can be used to investigate the effects of corrosion damage on the behavior of corroded steel members.